It is possible, but it may be quite difficult depending on the bridge. The AI's timer for when they can destroy the bridge is significantly shorter on higher difficulties.

The chance the bridge will actually blow when the AI tries to destroy it is determined by the number of bridge victory locations controlled by the Germans, and is unaffected by the difficulty setting. There are basically three ways to capture a bridge, in game terms:

1) Rush the bridge before the timer is up.

2) Capture most (or all) of the other VLs on your side of the river, then break the German's morale so you are awarded extra VL(s), and get the bridge.

3) Sneak up to the bridge VLs and take them before the Germans spot you. Best attempted at night, but difficult even then, as most bridges are quite exposed. Careful use of smoke or blinding the enemy with a flare may help.